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Help with Homework 1A.15

Posted: Sat Oct 12, 2019 7:56 pm
by Ellis Song 4I
1A.15 In the ultraviolet spectrum of atomic hydrogen, a line is observed at 102.6 nm. Determine the values of n for the initial and final energy levels of the electron during the emission of energy that leads to this spectral line.

Reading this question, I have no idea where to begin. Is the question asking at which energy level the initial and final energy level are? How would you do this and how do you know which equations to use?

Re: Help with Homework 1A.15

Posted: Sat Oct 12, 2019 8:14 pm
by Ada Chung 1C
Here is how I would approach the problem and kind of my thought process
1. Because the problem tells you that this is in the UV spectrum you would be able to know that n1=1 (from the Lyman series)
2. Since you are given the wavelength you can use wavelength x frequency=speed of light to find the frequency. Once you have found frequency you can then find and solve for n1 by plugging in the frequency you go into Rydberg equation which is v=R((1/1^2)-(1/n2^2)) now solve for n2

Re: Help with Homework 1A.15

Posted: Sat Oct 12, 2019 8:19 pm
by Alex Chen 2L
The line wavelength is your starting point. Using that, you should be able to find the frequency of that line of light, so you can use the equation E=hv to find the energy that the electron emitted as a photon. Furthermore, remember that because UV light has the highest energy of light, the electron has to make the largest jump in energy levels, meaning the final energy level will be n = 1. After that, you can use the emperical equation En = -hR/n^2 to determine the energy level of n = 1 and add that to the energy of the line of light (from E=hv) in order to solve for the intial energy level n through the emperical equation again.

Re: Help with Homework 1A.15

Posted: Sat Oct 12, 2019 8:32 pm
by Hannah Lee 2F
In the ultraviolet spectrum of atomic hydrogen, a line is observed at 102.6 nm. Determine the values of n for the initial and final energy levels of the electron during the emission of energy that leads to this spectral line.


First, you would find the change in energy (ΔE). The equations we know are: c = λv and E = hv. Since the wavelength is given, you could find E via E = hc / λ.
Therefore: E = (6.626 x 10-34 J s)(2.998 x 108 m/s) / (102.6 x 10-9 m) = 1.936 x 10-18 J
It's important to realize that energy is being emitted, which means the e- is transitioning from a higher to lower energy level, so ΔE < 0. (The energy of electrons can be either positive or negative, but the energy of photons emitted/absorbed must always be positive.) Therefore, ΔE = -1.936 x 10-18 J.

The problem indicates that the line is observed in the UV spectrum, so it deals with the Lyman series, which ends at n = 1 (nfinal = 1).
Efinal = -hR / nfinal2 = -(6.626 x 10-34 J s)(3.28984 x 1015 Hz) / 12 = -2.180 x 10-18 J

We can then plug in the values we found into the equation ΔE = Efinal - Einitial. So:
-1.936 x 10-18 J = -2.180 x 10-18 J - Einitial
Einitial = -2.180 x 10-18 J - (-1.936 x 10-18 J)
Einitial = -2.438 x 10-19 J = -hR / ninitial2
ninitial2 = -hR / -2.438 x 10-19 J = - (6.626 x 10-34 J s)(3.28984 x 1015 Hz) / (-2.438 x 10-19 J)
ninitial = 3, so the e- transitions down from the energy level n = 3 to n = 1.